Structure of vacancy-ordered single-crystalline superconducting potassium iron selenide

With single-crystal x-ray diffraction studies, we compare the structures of three samples showing optimal superconductivity: ${\mathrm{K}}_{0.775(4)}{\mathrm{Fe}}_{1.613(1)}{\mathrm{Se}}_2$, ${\mathrm{K}}_{0.737(6)}{\mathrm{Fe}}_{1.631(3)}{\mathrm{Se}}_2$, and ${\mathrm{Cs}}_{0.748(2)}{\mathrm{Fe}}_{1.626(1)}{\mathrm{Se}}_2$. All have an almost identical ordered vacancy structure with a ($\sqrt{5}$ × $\sqrt{5}$ × 1) supercell. The tetragonal unit cell, space group $I$4/$m$, possesses lattice parameters at 250 K of $a$ $=$ $b$ $=$ 8.729(2) Å and $c$ $=$ 14.120(3) Å, $a$ $=$ $b$ $=$ 8.7186(12) Å and $c$ $=$ 14.0853(19) Å, and at 295 K, $a$ $=$ $b$ $=$ 8.8617(16) Å and $c$ $=$ 15.304(3) Å for the three crystals, respectively. The structure contains two iron sites; one is almost completely empty while the other is fully occupied. There are similarly two alkali metal sites that are occupied in the range of 72.2(2)%–85.3(3)%. The inclusion of alkali metals and the presence of vacancies within the structure allows for considerable relaxation of the ${\mathrm{FeSe}}_4$ tetrahedron, compared with members of the Fe(Te, Se, S) series, and the resulting shift of the Se–Fe–Se bond angles to less distorted geometry could be important in understanding the associated increase in the superconducting transition temperature. The structure of these superconductors are distinguished from the structure of the nonsuperconducting phases by an almost complete absence of Fe on the (0 0.5 0.25) site, as well as lower alkali metal occupancy that ensures an exact ${\mathrm{Fe}}^{2+}$ oxidation state, which are clearly critical parameters in the promotion of superconductivity.

Figure 1

Panel (a) Single Crystal X-ray Diffraction pattern of ${\mathrm{K}}_{0.775(4)}{\mathrm{Fe}}_{1.613(1)}{\mathrm{Se}}_2$ showing the relationship between the original $\mathrm{Th}{\mathrm{Cr}}_2{\mathrm{Si}}_2$ cell of approximate dimensions 3.9 Å and 14 Å indicated by vectors $a_{\mathrm{B}}^{*}$ and $b_{\mathrm{B}}^{*}$ can be interpreted in ($5\times 5\times 1$) cell labeled, $a_{|\mathit{rm}p}^{*}$ and $b_{\mathrm{p}}^{*}$. Alternatively ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ represent two alternative twinned cell with ($\sqrt{5}\times \sqrt{5}\times 1$) as proposed by Haggstrom et al.[27] Panel (b) Diagramatic representation of the structure in real space showing the ($5\times 5\times 1$) cell (black) compared with the reduced ($\sqrt{5}\times \sqrt{5}\times 1$) cell (red).

Figure 2

Comparison of the (a) ${\mathrm{A}}_x{\mathrm{Fe}}_{1-x/2}{\mathrm{Se}}_2$ structure with the same body centered ThCr${}_2$Si${}_2$-type stacking as (b) BaFe${}_2$As${}_2$ rather than the primitive anti-PbFCl structure of (c) NaFeAs.

Figure 3

Structure of ${\mathrm{K}}_{0.775(4)}{\mathrm{Fe}}_{1.613(1)}{\mathrm{Se}}_2$ from the [001] direction in the ($\sqrt{5}\times \sqrt{5}\times 1$) cell showing fully occupied Fe sites (orange) decorated with ordered vacancy sites.